Application of Compressive Sensing to High-resolution Meteorological Observations with Imaging Radar

The observation of rapidly evolved severe weather requires high spatial and temporal resolutions. Imaging radars can provide much faster update time (~10 seconds) comparing to conventional weather radars (~a few minutes) by using digital beam forming (DBF) technique, in which multiple receiving beams are formed simultaneously within the field of view (FOV). The FOV is defined by the transmitted beam width, which is typically wide enough to cover the region of interest. Simultaneous receiving beams are generated by processing signals from spatially separated arrays of antennas. Several DBF methods (Fourier, Capon, etc.) have been developed to reconstruct reflectivity structure. However, high-resolution reliable power estimation for distributed targets like weather is still a challenge in DBF due to calibration, noise, etc.

The emerging technique of compressive sensing (CS) has been developed to recover sparse images exactly from much fewer incoherent measurements. It also has been shown theoretically that random measurements are largely incoherent with transformation matrix (such as Discrete Cosine Transform, Wavelet, etc.) and also robust to noise contamination. In this work, CS is applied to reconstruct high-resolution reflectivity from a limited number of receivers. Unlike DBF, the problem is formulated as a linear model. The assumption of sparsity of the reflectivity field in a transformation domain is verified. The impact of receiver configurations on the CS reflectivity estimation is investigated using simulations. Specifically, three receiver configurations of uniformly, non-redundantly and randomly samples for a fixed aperture size are performed for different conditions such as the number of receivers, signal-to-noise-ratio (SNR), and the number of samples. In simulation, complex time series signals are generated from 3-D radar simulator based on realistic fields generated from Advanced Regional Prediction System. The performance of CS is quantified by the root-mean square error and compared to the results from Fourier and Capon DBF techniques. Preliminary results show that CS can provide relatively high-resolution and reliable reflectivity reconstruction for most cases. Furthermore, the feasibility of CS is demonstrated using data from the Atmospheric Imaging Radar (AIR), designed and built in the Advanced Radar Research Center (ARRC) at the University of Oklahoma.